(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the set of all n x n matrices A such that AB = BA for a fixed n x n matrix B, is a subspace of M_{nn}.

2. Relevant equations

u+vis in the same vector space asuandv.

kuis in the same vector space asu, wherekis any real number.

3. The attempt at a solution

I am drawn to think of a diagonal matrix when I think of this question. And if I multiply a diagonal matrix by a scalar, it can only be a diagonal matrix or the zero matrix, either way, it AB still equals BA. Similarly, adding two diagonal matrices obtains either another diagonal matrix or the zero matrix...so, in this way, A is a subspace of M_{nn}.

Am I correct?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proving a subspace

**Physics Forums | Science Articles, Homework Help, Discussion**